1. Field of the Invention
The invention is related generally to the field of electrical resistivity well logging methods. More specifically, the invention is related to methods for determining resistivity values in a multi-component induction measurement in highly-deviated wells.
2. Description of the Related Art
Electromagnetic induction and wave propagation logging tools are commonly used for the determination of electrical properties of formations surrounding a borehole. These logging tools give measurements of apparent resistivity (or conductivity) of the formation that, when properly interpreted, reasonably determine the petrophysical properties of the formation and the fluids therein.
The physical principles of electromagnetic induction resistivity well logging are described, for example, in H. G. Doll, Introduction to Induction Logging and Application to Logging of Wells Drilled with Oil-Based Mud, Journal of Petroleum Technology, vol. 1, p. #148, Society of Petroleum Engineers, Richardson, Tex. (1949). Many improvements and modifications to electromagnetic induction resistivity instruments have been devised since publication of the Doll reference,. Examples of such modifications and improvements can be found, for example, in U.S. Pat. No. 4,837,517; to Barber, U.S. Pat. No. 5,157,605 issued to Chandler, et al.; and U.S. Pat. No. 5,452,761 issued to Beard, et al.
A typical electrical induction instrument is described in U.S. Pat. No. 5,452,761 (Beard.) The induction logging instrument described in Beard includes a number of receiver coils spaced at various axial distances from a transmitter coil. Alternating current is passed through the transmitter coil, which induces alternating electromagnetic fields in the earth formations. Voltages, , are induced in the receiver coils as a result of electromagnetic induction phenomena related to the alternating electromagnetic fields. A continuous record of the voltages form curves. These curves are also referred to as induction logs. Induction instruments that are composed of multiple sets of receiver coils are referred to as multi-array induction instruments. Every set of receiver coils together with the transmitter is considered as a subarray. Hence, a multi-array induction tool comprises numerous subarrays and acquires measurements with all the subarrays.
Voltages induced in axially more distal receiver coils are the result of electromagnetic induction phenomena occurring in a larger volume surrounding the instrument, and voltages induced in axially proximal receiver coils are the result of induction phenomena occurring more proximal to the instrument. Therefore, different receiver coils see a formation layer boundary with different shoulder-bed contributions, or shoulder-bed effects. The longer-spaced receiver coils see the formation layer boundary at further distance from the boundary than the shorter-spaced receiver coils do. As a result, the logs of longer-spaced receiver coils have longer shoulder-bed effects than the logs of shorter-spaced receiver coils. The logs of all the receiver coils form a certain pattern.
Variations of measurements with azimuthal angle can be corrected. If the layers are not perpendicular to the axis of the instrument, the conductivity of the media surrounding the instrument can vary with azimuthal angle, causing any inferences about the conductivity from the measurements of the induction voltage to be in error. A method for correcting this error is described in U.S. Pat. No. 5,774,360 issued to Xiao and Zhou. The method requires the relative dip angle as a priori information. The relative dip angle is the angle between the borehole axis and the normal of the bedding plane. Because the formation layers can also be inclined, the relative dip angle is normally unknown even though the wellbore deviation is known. U.S. Pat. No. 6,049,209 issued to Xiao and Geldmacher teaches another method that has also been developed to interpret induction logs in environments of relative inclination and anisotropy. The method requires the relative dip angle and the anisotropy coefficient as a priori information. The anisotropy coefficient can be defined as the ratio between the resistivity perpendicular to bedding and the resistivity parallel to bedding.
A limitation to the electromagnetic induction resistivity well logging instruments known in the art is that they typically include transmitter coils and receiver coils wound so that the magnetic moments of these coils are substantially parallel only to the axis of the instrument. Eddy currents are induced in the earth formations from the magnetic field generated by the transmitter coil, and in the induction instruments known in the art. These eddy currents tend to flow in ground loops which are substantially perpendicular to the axis of the instrument. Voltages are then induced in the receiver coils related to the magnitude of the eddy currents. Certain earth formations, however, consist of thin layers of electrically conductive materials interleaved with thin layers of substantially non-conductive material. The response of the typical electromagnetic induction resistivity well logging instrument will be largely dependent on the conductivity of the conductive layers when the layers are substantially parallel to the flow path of the eddy currents. The substantially non-conductive layers will contribute only a small amount to the overall response of the instrument, and therefore their presence will typically be masked by the presence of the conductive layers. The non-conductive layers, layers which are typically hydrocarbon-bearing, are of the most interest to the user. Some earth formations which might be of commercial interest therefore may be overlooked by interpreting a well log made using conventional electromagnetic induction resistivity well logging instruments. The thin layers may correspond to geologically distinct intervals, yet if the laminations are beyond the resolving capability of the logging instrument, it would appear as a single layer (for geophysical purposes). Hence for the purposes of this invention, the term “layer” could include both geological layers and geophysical layers.
U.S. Pat. No. 5,999,883 issued to Gupta, et al., (the “Gupta patent”), the contents of which are fully incorporated herein by reference, discloses a method for determining the horizontal and vertical conductivity of anisotropic earth formations. Measurements are made of electromagnetic signals induced by induction transmitters oriented along three mutually orthogonal axes. One of the mutually orthogonal axes is substantially parallel to a logging instrument axis. The electromagnetic induction signals are measured using first receivers each having a magnetic moment parallel to one of the orthogonal axes and using second receivers each having a magnetic moment perpendicular to one of the orthogonal axes which is also perpendicular to the instrument axis. A relative angle of rotation of the perpendicular one of the orthogonal axes is calculated from the receiver signals measured perpendicular to the instrument axis. An intermediate measurement tensor is calculated by rotating magnitudes of the receiver signals through a negative of the angle of rotation. A relative angle of inclination of one of the orthogonal axes which is parallel to the axis of the instrument is calculated, from the rotated magnitudes, with respect to the direction of the vertical conductivity. The rotated magnitudes are rotated through a negative of the angle of inclination. Horizontal conductivity is calculated from the magnitudes of the receiver signals after the second box of rotation. An anisotropy parameter is calculated from the receiver signal magnitudes after the second box of rotation. Vertical conductivity is calculated from the horizontal conductivity and the anisotropy parameter.
Shoulder bed corrections related to the effect of formations above and below the depth being evaluated also have to be applied to the data. Methods for making these corrections to data acquired with conventional logging tools are well known in the art. For example, U.S. Pat. No. 5,446,654 to Chemali teaches the conversion of a resistivity log as a function of well depth into a rectangularized curve so that the interfaces of the adjacent strata are located, and a suitable number of iterations, a correction factor is applied. The corrected rectangular log is obtained with a correction coefficient computed at each depth. For each computation, the impact of all the strata within a specified depth window is considered, while strata beyond that window are simplified by representing the strata beyond the window with single equivalent bed values to reduce the number of computations required. This then provides a resistivity log which is substantially free of shoulder bed effect.
The method of U.S. Pat. No. 5,867,806 to Strickland, et al. corrects for shoulder bed effect in LWD resistivity logs through inversion. The method selects one or more control depths at one or more locations of each of a plurality of detected beds in the formation. The method then estimates the resistivity of each bed only at the selected control depths to produce an estimated resistivity of the beds. The method then computes a simulated log value at each control depth using a current estimate of the resistivity of the beds. The computer-simulated log is then computed to the actual log data at each control depth, and the resistivity of each bed is adjusted using the difference between the actual and simulated values at the control depths. The method iteratively repeats a plurality of times until the simulated log substantially matches the actual log at the control depths.
Electrically anisotropic reservoirs are encountered frequently in hydrocarbon exploration. For accurate saturation estimation and optimum hydrocarbon recovery from these reservoirs, it is essential to detect and properly describe their electrical properties. For example, in laminated sand-shale sequences or sands with different grain size distributions, the vertical resistivity (perpendicular to the bedding) is more indicative of the hydrocarbon content than the horizontal resistivity (parallel to the bedding). However, the response measured by conventional induction tools with their transmitter-receiver coil moments oriented normal to bedding is dominated by the horizontal resistivity. Therefore, a petrophysical evaluation based on these data can either overlook hydrocarbons present in laminated sands or underestimate their productivity.
The relative formation dip angle is vital for proper and accurate interpretation of data acquired by the new multi-component induction instrument. This newly developed induction instrument comprises three mutually orthogonal transmitter-receiver arrays. These configurations allow us to determine both horizontal and vertical resistivities for an anisotropic formation in vertical, deviated, and horizontal boreholes. A description of the tool can be found in U.S. Pat. No. 6,147,496, to Strack, et al. The transmitters induce currents in all three spatial directions and the receivers measure the corresponding magnetic fields (Hxx, Hyy, and Hzz,). In this nomenclature of the field responses, the first index indicates the direction of the transmitter and the second index denotes the receiver direction. As an example, Hzz is the magnetic field induced by a z-direction transmitter coil and measured by a z-directed receiver. The z-direction is parallel to the borehole. In addition, the instrument measures all other cross-components of the magnetic fields, i.e., Hxy, Hxz, Hyx, Hyz, Hzx, and Hzy.
The signals acquired by the main receiver coils (Hxx, Hyy, and Hzz) are used to determine both the horizontal and vertical resistivity of the formation. This is done by inverse processing techniques of the data. These inverse processing techniques automatically adjust formation parameters in order to optimize in a least-square sense the data match of the synthetic tool responses with measured data. Required inputs in this process are accurate information of the relative formation dip and relative formation azimuth. This information can be derived using, in addition to the main signals (Hxx, Hyy, and Hzz), the data from the cross-components. In highly deviated wells (70° or higher), skin-depth-corrected single frequency Hxx+Hyy measurements depend largely on the horizontal resistivity of the formation. The sum of dual frequency Hxx+Hyy measurements also mainly depends on the horizontal resistivity of the formation.
Prior methods are useful in determining resistivity values in wells where the angle of deviation from vertical is substantially less than 70 degrees. Typically, errors in conductivity values appear in highly-deviated wells. There is a need for a method that obtains a resistivity value in highly-deviated and horizontal wells. The present invention fulfills that need.